Blender 2.9 - how to delete animation action?
You can delete them the way you're trying to, maybe it moves your object as it is not transformed by the action anymore:

You can also go in the Outliner, choose Display Mode &gt; Blender File and under Actions, delete the actions you want with a left click &gt; Delete:

Also, if you press Shift and the X button on the right of the action name in the Dope Sheet, it will be marked as 0 (no user), it won't be saved when you'll close your file and in the Outliner &gt; Display Mode &gt; Orphan Data it will be displayed as orphan and you can delete it immediately if you want: